Scolari Vittore (Institut Curie)

Forces shaping chromatin in the nucleus

The physics of genome dynamics requires innovative out-of-equilibrium approaches because the cell nucleus, from the most basic chemical reactions to evolutionary timescales of billions of years, strives to counteract disorder in order to be healthy, consuming energy, being alive. My objective is to develop a physical theory able to describe intranuclear dynamics, with the ambition of reaching a quantitative understanding of the two essential processes of gene regulation and DNA recombination. In particular, I investigate: (i) how 3D chromosome conformation is shaped by specific biological processes. Particularly loop extrusion and the formation of foci – or phases – for heterochromatin and transcription, and (ii) the fundamental implications of thee mechanisms on control and reliability of the biological processes of transcriptional induction, gene silencing, and evolution. In this talk I will present my original approach to simulate loop extrusion, an active process central in regulating the shape of chromatin in vivo. The “gold standard” currently uses molecular dynamics simulations: while very flexible, this limits our possibility (i) to explore the parameter space in an efficient manner and (ii) to dissect the observed effects under the lenses of a coherent analytical theory. I will show my original approach that exploits the analytical solution of the Einstein-Smoluchowski equation for the Rouse model affected by the action of extruders simulated in 1D. The resulting probability distributions highlight the hallmarks of the out-of-equilibrium processes on chromatin conformation observed in vivo by experiments. Finally, this approach permits the definition of the Gibbs entropy of chromosome conformation. I will show how the application of this concept to simplified toy-models increases our analytical understanding of the loop extrusion process. Finally, I will present my future scientific plans.

Marcel Filoche (École Polytechnique)

The landscape of wave localization

In disordered systems or in complex geometry, standing waves can undergo a strange phenomenon that has puzzled physicists and mathematicians for over 60 years, called “wave localization”. This localization, which consists of a concentration (or a focusing) of the energy of the waves in a very restricted sub-region of the whole domain, has been demonstrated experimentally in mechanics, acoustics and quantum physics. We will present a theory which brings out an underlying and universal structure, the localization landscape, solution to a Dirichlet problem associated with the wave equation [1]. In quantum systems, this landscape allows us to define an “effective localization potential” which predicts the localization regions, the energies of the localized modes, the density of states, as well as the long-range decay of the wave functions. This theory holds in any dimension, for continuous or discrete systems. We will present the major mathematical properties of this landscape. Finally, we will review applications of this theory in mechanics, semiconductor physics, as well as molecular and cold atom systems.

[1] M. Filoche & S. Mayboroda, Proc. Natl Acad. Sci. (2012) 109:14761-14766.

Guillaume Roux (LPTMS, Université Paris Saclay)

Coexistence and phase separation of pairs and fermions in a one-dimensional model with pair-hopping

We consider a simple model of spinless fermions in which the kinetic energy competes with a pair-hopping term. We show by means of numerical calculations that there exists a phase in which part of the fermions are paired while the others remain unpaired. These elementary components makes two mixed Luttinger liquids, one for pairs and one for fermions. A simple two-fluid model accounts remarkably well for the observed numerical data. Adding nearest-neighbour interaction leads to a rich phase diagram in which we observe a regime in which the two previous Luttinger liquids get phase separated. In the context of impurity physics, this model on a finite size chain allows for the creation of a single pair interacting with a fermionic bath or a single fermion interacting with a paired fermions bath.

Alessio Squarcini (Max-Planck-Institute for Intelligent Systems, Stuttgart)

Long-range medium-mediated interactions: two exactly solvable models

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In this talk I will discuss two situations in which long-range effects such as ordering and forces emerge in certain systems of classical statistical mechanics and how such models are handled through exact techniques.

The first part of my talk revolves around the following question: can order extend over distances larger than the bulk correlation length? I will show how a network of Ising boxes connected by channels is able to exhibit an extraordinarily long-range ferromagnetic order over distances which grow exponentially with the cross sections of the channels. The emergence of such a new length scale follows from an exact calculation based on the diagonalization of the transfer matrix for the square lattice Ising model. The analytical study is flanked by extensive Monte Carlo simulations [1].

The second phenomenon I will discuss is the critical (or thermodynamical) Casimir effect [2]. Chemically inhomogeneous colloidal particles immersed in a critical binary mixture are subjected to a fluctuation-induced-force known as the critical Casimir effect. By modeling a binary mixture at its demixing critical point by means of the critical Ising model in two dimensions, and exploiting its scaling limit description in terms of a Conformal Field Theory, I determine the exact density profiles and correlation functions around various particles whose boundaries are formed by patches with different chemical structure and preference of the binary mixture components. The formalism encompasses several interesting configurations, including Janus particles, colloidal quadrupoles and needles with inhomogeneous patches of symmetry breaking boundary conditions. Within the framework of the ‘’Small Particle Operator Expansion’’ I determine the exact asymptotic behavior of the interaction free energy between these colloids, and colloids confined by a wedge-shaped wall. The theoretical predictions are confirmed by numerical results available in the literature.

References
[1] D. B. Abraham, A. Maciolek, AS, and O. Vasilyev, Action at a distance in classical uniaxial ferromagnetic arrays, Phys. Rev. E 96, 042154 (2017).
[2] AS, A. Maciolek, E. Eisenriegler, and S. Dietrich, Critical Casimir interaction between colloidal Janus-type particles in two spatial dimensions, J. Stat. Mech. 043208 (2020).